Ray-tracing Diagnostics

8/22/01
Problems with the SPARO tertiary template, or are they?.

This report details the current state of the investigations into the beam size
discrepancy via the condensing mirror of the SPARO setup of the Viper telescope.
The problem detailed in the initial report seem to be
primarily a result of our reliance that the CR ray on the template was the
center ray in a supplied ray trace file (1.3 m OA ray) and an important sign
flip on one of the vectors. After a number of
confusing results detailed elsewhere we now realize
that the template CR is not the 1.3m OA ray, and that we should define our
coordinates relative to something more definite (the chopper).
This report mimics and extends the previous
analysis using the 1.35 m OA ray that is the real center ray for the Viper
system (and possibly the SPARO/Viper template). We show that the difference
in the angle of incidence at the Condensing (marked as tertiary) mirror in
the initial report disappears.

The measurements involve tracing the central ray in both BEAM3
and then manually on the stainless steel template that was made in 1998
at CMU using this information. It is now known that the 'CR' marked on the
template was drawn by Tom Renbarger of NU while at Pole, useing a mark on the
secondary indicating the position of the central ray.

Based on the work of the past few months, two sets of measurements with the template
are possible.

Using a coordinate system to measure the points of impact with the various
surfaces (secondary, chopper, etc.), and translating them into the
system used in Beam4. This translation is indicated here.
It is then possible to determine the distances between the points (the
optical path length) and the angles between the incident and reflected
rays, using the dot-product of the normalized vectors. The uncertainties
in the position measurements are unknown, but are likely around a few
millimeters.

Physically measuring the OPL with a meterstick on the template. These measurements
are accurate to with in several (less than 5) millimeters. The angles between
incident rays are measured with a protractor, to an accuracy of ~1 degree (due
to the overly wide ray markings).

Measurements in Beam4 are made using the InOut command in the ray table, using the P (OPL
variable) and the vector variables (U,V,W) at each surface. To find the difference between
the chopper and the condensing mirror (surfaces 3 and 4 in the optics table above) you
simply use OPL=P4-P3. Similarly, the angle of incidence at the chopper is arccos( * ),
where * is the scalar product of the two vectors.

For the determination of angles using the scalar product to find the cosine, it is highly important
to make sure the vectors are tail to tail. Normally, this error is easy to catch. However in the
October report, the angle at the condensing mirror was very close to 90 degrees, leading us to a
false conclusion. Therefore, special care was taken in this analysis.

Angle of Incidence for the Central Ray (degrees)
Using method 1. above

Measured:

BEAM3:

Difference:

Secondary:

20.5697

20.5558

0.013873

Chopper:

32.8452

33.6104

-0.7652

Condensing:

47.673

47.317

0.356

Path difference between surfaces (cm)
Using method 1. above

Measured:

BEAM3:

Difference:

Prime Focus to Secondary:

58.92 cm

58.9162 cm

0.0038 cm

Secondary to Chopper:

63.5125 cm

63.626 cm

-0.1135 cm

Chopper to Condensing:

56.379 cm

55.814 cm

-0.565 cm

Angles of incidence (degrees)
Using method 2. above

Measured:

BEAM3:

Difference:

Secondary:

20.55

20.5558

-0.00585

Chopper:

32.55

33.6104

-1.0604

Condensing:

47.25

47.317

-0.067

Path difference between surfaces (cm)
Using method 2. above

Measured:

BEAM3:

Difference:

Prime Focus to Secondary:

58.65 cm

58.9162 cm

-0.2662 cm

Secondary to Chopper:

63.45

63.626 cm

-0.176 cm

Chopper to Condensing:

55.5 cm

55.814 cm

-0.314 cm

Investigations of other files on disk reveal that this is, in fact the
setup that bears the closest resembelence to the template. Secondly,
we are doubly sure this is the correct optical setup for SPARO in that
0.7 meters of the primary are illuminated
by a focused beam, just like the real telescope.

Thus, after comparing with the original report, the anaomolies at the
condensing mirror are no longer present, regardless of how the points
are measured. In terms of accuracy, the first method is probably more
accurate, but by both measures, the parameters on the condensing mirror
are well within the boundaries established by the other surfaces.
Investigations are ongoing, however.